Here is my last and final proposal: a sequence of 8290 primes out of 8363 candidates.
There is a cycle going from 13597 to 83597 with 8149 elements.
JPF
I'm preparing a "dictionary" of five letter words that I downloaded from the Zyzzyva site and I'm bowdlerizing it (I won't be using any bad language or other offensive terms on this or any other forum - for those unfamiliar with the Scrabble world
all swear words and other offensive terms such as racial epithets are allowed in Scrabble tournaments and so are included in Scrabble word lists). That way the results won't depend on who's been clever enough to find the right dictionary.
If you are interested in participating in this project please let me know and I'll upload the dictionary.
JPF wrote:Hi, Leren
Congratulations for your findings!
I admire your perseverance to solve this problem.
Finding a Hamiltonian path in a large graph is challenging, but I must admit I was not really motivated by finding paths among prime numbers
I have also read the article you mentioned, but I didn't implement all the (complex) algorithm. I only kept the following idea:
"For each unvisited neighbor w of vr, compute η(w), the number of unvisited neighbors of w. Select vr+1 = w such that η(w) is a minimum "
I randomly selected a minimum.
I finally turned off my computer after reaching 8290 because progress was too slow.
JPF
PS: It's funny to see that Guenter Stertenbrink (dukuso in the sudoku's World) is indirectly involved in that paper.